r-Fold Multivectors and Superenergy

A general structure combining Grassmann, Clifford and tensor products is presented. The r -fold multivectors provide the basis for the natural extension of Grassmann and Clifford algebras when several geometric entities are multilinearly related. Any tensor can be organized and understood as an r -fold multivector when its antisymmetries are taken into account. The r -fold Clifford algebra is contrasted with the multiparticle geometric algebra. The application of r -fold Clifford algebra to the study of superenergy tensors in physics is shown to provide their simplest definition. In addition, it constitutes a most efficient tool for obtaining and proving their essential properties, such as dominant positivity and conditions for their conservation.